The string spacing looks super off at the nut. Some strings seem to be very close and others further apart, or am I trippin'?

It's fanned. The spacing at both the nut and the bridge will almost always be equal center-to-center of the strings. Parallel frets can get away with proportional spacing at the nut and equal spacing at the bridge. You can have proportional spacing at the nut with a fanned-fret guitar, but you have to keep the same proportions along the line of the bridge, which makes things weirdly spaced at the bridge.

Ray

The Ultimate Question: What string gauge is needed for 18.84# of tension when tuned to E2 on a 27" scale guitar?

It's fanned. The spacing at both the nut and the bridge will almost always be equal center-to-center of the strings. Parallel frets can get away with proportional spacing at the nut and equal spacing at the bridge. You can have proportional spacing at the nut with a fanned-fret guitar, but you have to keep the same proportions along the line of the bridge, which makes things weirdly spaced at the bridge.

Ray

No, I think he meant at the nut (or lack of nut). Since there's no nut the strings are just lining up with the tuning pegs, which has them at varying distances from each other. My guess is that it WILL have a nut, he just hasn't put it on yet. Might be a zero fret and a string guide, but something will be going there.